Subtraction



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For tips and tricks on subtraction please see: Subtraction Tips and Tricks

For beginning subtraction worksheets that cover subtracting single-digit whole numbers and contain subtraction problems such as 1-1, 2-2, 3-0, and 4-2 see: Beginning Subtraction
#1 #2 #3.

For three subtraction worksheets that cover subtracting a single-digit whole number from another single-digit whole number and contains problems such as 4-2, 6-3, 9-7, and 8-5 see: Subtracting Single Digit Whole Numbers
#4 #5 #6.

For three subtraction worksheets that covers problems like 10-2, 27-3 and 89-9 see: Subtracting One-Digit Whole Numbers from Two-Digit Whole Numbers
#7 #8 #9.

For three subtraction worksheets that covers problems such as 1128, 456-32 and 500-200 see: Subtracting One, Two and Three-Digit Whole Numbers from Three-Digit Whole Numbers
#10 #11 #12.

This new subtraction probe/test covers the above problems and should be a fair assessment of one, two, three and four-digit whole number subtraction with and without borrowing or renaming:
Subtraction Test.

Introduction

Subtraction is one of the four basic arithmetic operations. It is actually the inverse of addition. Subtraction is denoted by minus sign “-” in infix notation. It is process, which has a different way of teaching in different countries. Moreover, it also changes from time to time even within a country. The traditional mathematics taught children with multi digit numbers.

Terms in subtraction

There are mainly two terms in subtraction, one is the “minuend” and the other is “subtrahend”. The number from which another value will be subtracted is called the minuend and the value that is subtracted is called the subtrahend.

Details about American and Austrian school of subtraction

American schools have adopted a system of borrowing and a system of markings called crutches to teach subtraction. Among the two, the method of crutches is the newer one and is invented by William A. Browell. It got great mileage in popularity and was successful in displacing the other methods, prevalent in America during that time.

The European opted for the Austria method to teach their children. This is also called the addition method and doesn't involve any borrowing. Though this process also involves crutches but they vary from country to country.

For instance in case of a subtraction like 705 - 295, the minuend is 705 and the subtrahend is 295. In case of the American process, whenever any number in the minuend is lesser than the subtrahend then that value is increased by 10 and to compensate the increment, it decreases the value of the next digit by 1. For instance, in case of the above subtraction the 0 in the tenth place of the minuend is lesser than 9 of the subtrahend. Therefore, 0 is treated as 10 as it is increased by 10. However, to compensate it, the digit in the hundredth place of the minuend that is 7 will be reduced by 1 and will be treated as 6. This constitutes the American system. The basic difference between the American and the Austrian process is that in the Austrian process the value of the digit in the hundredth place of the subtrahend that is 2 will be increased by 1 and will be treated as 3.

Uses of subtraction